Hello Amrit,
You wrote: "Time has only a mathematical existence."
My work involves developing methodology for multidiscipline-spanning transdisciplinary understanding that enhances communication between the disciplines. To develop the methodology it is necessary to examine and compare the real-world subject matters of the various disciplines.
Part of the procedure for comparing the subject matters of the disciplines is to ask certain specific questions that are particularly useful for focusing the analysis
When analyzing the intrinsic nature of something that exists, I ask What is it?, Where is it?, and What is it made of? I ask these questions about the subject matter of every discipline.
The first question, What is it?, is usually the initiator for the analysis: What is time?
Your answer to that question is that time exists only with the math.
The next questions then are (1) What is math?, (2) Where is math? and (3) What is math made of?
(1) What is math? Math is an artificial man-made construct, a tool that is used to work with quantities, a tool that enables the process of interrelating quantities.
Everything that exists has quantitative aspects of that existence--how big it is; how much matter it is composed of; how long it exists; how many subcomponents it has; and so on. Naturally existing things, rocks, crocodiles, stars, while they have many quantitative aspects of their existence, they do not have mathematical aspects of their existence. Math does not play any roles in their origins, structures, or processes.
(2) Where is math? Existing as a man-made artifact, math occurs only where humans and human artifacts occur. Math occurs within the minds of humans. It occurs as symbols written in pencil, ink, or some other medium suitable for writing on paper, blackboards, or some other surface suitable for writing symbols. It occurs in computers and their algorithms. And it can occur in other situations that humans create, such as a process, the sequential manipulation of the beads on an abacus for example.
If you look to see where in the universe humans and their artifacts occur, it is observationally evident that the distribution of humans and their artifacts is extremely limited--restricted to the solar system. The solar system looks big from the personal human viewpoint, but it is only one of many such systems that we now know about scattered throughout an immense region of space.
Time occurs throughout that immense region. It is possible to watch a distant star, and observe that it not only exists, but that it continues to exist with time as the observation continues.
Time can be observed to occur beyond the limits of the region of space, the solar system, where math is used as a tool by humans. Math is too limited in its distribution to account for the much greater observable distribution of the occurrence of time.
Math is inadequate as a basis of time in the universe.
(3) What is math made of?
There are two fundamental modes-of-being, two foundational ways something can exist--immaterial and material.
Space and time are immaterial. Everything else that is known to exist has a material (substantial) basis to its existence.
When observing space and matter, it can be seen that matter occupies space. Space provides an existential-context, a place-to-be, for matter. Space exists as the extension of three-dimensional spatial-place.
Spatial-place appears to be immaterial. The role of space of providing a place in which matter can exist does not require that space be a medium of any sort. Spatial-place does not require a material basis for its existence.
To ascribe a material basis for space is anthropomorphic, and anthropomorphism is disallowed in science.
Everything else that is known to exist has, and requires, some form of material basis to its existence.
For example, processes are sequences of interrelations between material components.
Mathematical procedures are processes of interrelating mathematical symbols. To exist, those symbols require a material basis. Math only exists where its material basis exists--brains, ink, chalk, blackboards, computers, abacuses, and so on. All the known material bases of mathematical procedures exist within the solar system.
The known distribution of the material basis of math is too limited to provide a basis of time in the universe.
There is a paper at ResearchGate and at Academia.edu that reports the identification of the basis of time in the universe. This paper explains what time is, making it clear why time is not based in any way on math.
Vesterby, Vincent. 2014. The Identification of the Intrinsic Nature of Time.
https://www.researchgate.net/publication/299437469_The_Identification_of_the_Intrinsic_Nature_of_Time
Vesterby, Vincent. 2014. The Identification of the Intrinsic Nature of Time.
https://www.academia.edu/21710898/The_Identification_of_the_Intrinsic_Nature_of_Time
Regards,
Vincent